Number shortener

shortNum.js

function shortNumber (num, desiredDigits) {
  if (num < 0) {
    // Negative
    return '-' + shortNumber(-num, desiredDigits-1);
  } else if (num === 0) {
    // Zero is problematic
    return '0';
  }

  function standardNotation (num, desiredDigits) {
    const digitsAboveZero = Math.ceil(Math.log10(num));
    if (num !== Math.floor(num)) --desiredDigits; // has decimal point
    // Round off unwanted digits
    const divisor = Math.pow(10, desiredDigits - digitsAboveZero);
    const roundNum = Math.floor(num * divisor + 0.5) / divisor;
    if (num < 1.0) {
      // Cut off 0 for 0.x
      return roundNum.toString().slice(1);
    } else {
      return roundNum.toString();
    }
  }

  function scientificNotation (num, desiredDigits) {
    const exponent = Math.floor(Math.log10(num));
    const estr = 'e' + exponent; // exponent string
    const divisor = Math.pow(10, exponent);
    const mantissa = standardNotation(Math.floor(num / divisor), desiredDigits - estr.length);
    return mantissa + estr; // Concat!
  }

  function fallbackNotation (num) {
      return num < 1 ? '0' : '∞';
  }

  const standard = standardNotation(num, desiredDigits);
  if (standard.length <= desiredDigits) return standard;

  const scientific = scientificNotation(num, desiredDigits);
  if (scientific.length <= desiredDigits) return scientific;

  return fallbackNotation(num);
}

const testCases = [
  [0, 5, '0'],
  [500, 5, '500'],

  [1/3.0, 5, '.3333'],
  [1/3.0, 2, '.3'],
  [-1/3.0, 5, '-.333'],
  [-1/3.0, 3, '-.3'],

  [55.555, 3, '56'],
  [55.555, 4, '55.6'],
  [55.555, 5, '55.56'],

  [5000, 3, '5e3'],
  [500, 2, '∞'],
  [-500, 2, '-∞'],
  [0.05, 3, '.05'],
  [0.0005, 3, '0'],
  [-0.0005, 3, '-0'],
  [0.0005, 4, '5e-4'],
  [-0.0005, 5, '-5e-4'],
];

testCases.forEach((([num, desiredDigits, expected]) => {
  const result = shortNumber(num, desiredDigits);
  if (result !== expected) {
    console.log(result, expected);
  }
}));